Well, for instance, Naruto could meet Brian the dog. Brian, being intelligent, could have deep conversations with Naruto about their different worlds and values. Naruto could share his dreams of becoming Hokage and Brian could talk about his writing aspirations. It would be an interesting exchange of ideas between a ninja and a talking dog.
The Griffin family would likely react in different ways. Lois would probably try to be the peacemaker and make Inuyasha feel welcome. Chris might be in awe of Inuyasha's strength and cool sword. Meg could see Inuyasha as someone who doesn't fit in, just like her, and they could form an unlikely friendship. Meanwhile, Inuyasha would be constantly on guard, not fully understanding the intentions of these strange new people. He might mistake some of their jokes for real threats and react accordingly, which would lead to some very funny situations.
The characters would probably be very confused at first. For instance, Stan might look at Peter Griffin like he's some kind of alien. But then they could start to bond over things like their love for junk food.
They could start by mistaking each other for enemies. For instance, when Naruto first meets Yato, he might think Yato is some kind of new - type of ninja using strange powers. Yato, on the other hand, could be confused by Naruto's strange appearance and chakra. But then they realize they have a common goal, like protecting innocent people.
They can interact through battles. For instance, Naruto might face off against Thor in a friendly spar. Naruto's speed and agility could be pitted against Thor's strength and lightning powers.
They could interact through a portal that connects their two worlds. Naruto characters might be curious about the Kryptonians' superpowers and advanced technology. The Kryptonians, on the other hand, could be intrigued by the concept of chakra. For example, Superman (from Krypton) could teach Naruto about using his powers in a more controlled way, while Naruto could show Superman some of his cool ninjutsu moves.
Interaction can also happen in a more peaceful way. A Monster Musume who is good at cooking could share her recipes with Naruto and his friends. This would lead to cultural exchange as Naruto and his pals introduce her to ninja food. And they could exchange stories about their respective worlds over a meal.
Interaction could also happen in a school setting. If the Naruto characters somehow end up in the Highschool DxD school, they could join classes, participate in school activities, and make friends or enemies with the local students. There could be a lot of humorous situations as Naruto's more straightforward and energetic nature clashes with the more complex social dynamics of the Highschool DxD school.
They could start by trying to communicate. Since Majin Buu is often driven by his desires, the Naruto characters might try to use food or some form of entertainment to get his attention and start a conversation.
In fanfiction, the characters can interact in many ways. One way is if a Pokemon has some sort of healing ability and it tries to help Naruto with the negative effects of the Nine - Tails' chakra. Or, a Pokemon that can sense emotions might be able to communicate with the Nine - Tails on a deeper level. Also, Naruto could teach Pokemon some ninja - like moves, and in return, Pokemon could show Naruto new ways to use the Nine - Tails' power for non - combat purposes, like using its chakra for energy sources similar to how some Pokemon can generate electricity or heat.
Naruto would probably be very curious about the Adam's Family. He's used to a world of ninjas, so their spooky and unique lifestyle would be quite a shock at first. He might start by asking a lot of questions. And the Adam's Family would be equally curious about Naruto. Morticia might be interested in his ninja gear and how it compares to their own macabre accessories.